Module nested_dissection 

Nested dissection ordering for sparse direct solvers.

Provides graph-based fill-reducing orderings that minimize fill-in during sparse Cholesky or LU factorization. The main algorithm recursively finds vertex separators to split the graph, orders each partition recursively, then places separator vertices last.

Algorithm

1. Build an AdjacencyGraph from a symmetric CSR matrix.
2. Call NestedDissectionOrdering::compute to obtain a Permutation.
3. Evaluate quality with analyze_ordering.

The separator finder uses a multi-level approach: heavy-edge coarsening, BFS-based bisection on the coarse graph, and Fiduccia-Mattheyses refinement.

Structs

AdjacencyGraph

Undirected graph of a symmetric sparse matrix in CSR-like form.

MinimumDegreeOrdering

Approximate minimum degree ordering for small subgraphs.

NestedDissectionOrdering

Nested dissection ordering algorithm.

OrderingQuality

Quality metrics for an ordering.

Permutation

A permutation with its inverse, for reordering matrix rows/columns.

SeparatorResult

Result of a graph separator computation.

VertexSeparator

Finds graph vertex separators using a multi-level approach.

Functions

analyze_ordering

Analyze the quality of an ordering by estimating fill-in via symbolic factorization.